Svetlana Jitomirskaya, UCI Department of Mathematics, University of California Irvine

ArXiv (42) : Anti-resonances and sharp analysis of Maryland localization for all parameters, 2022
•  Logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators with smooth potentials, 2021
Homepage(s): CV- PDF, Quantum dynamics, hidden singularity, gap continuity

First email: Sunday, November 6, 2022 at 4:17 PM

Dear Prof. Dr. Svetlana Jitomirskaya:

I have been searching in the foundations of geometry for anything to do with quantum theory, fluctuations, spheres and transformations.

Have you seen a geometric combination like this: https://81018.com/15-1/  The top is composed of five tetrahedrons sharing at least one edge and a common centerpoint. In the middle are five octahedrons sharing at least one edge and the same centerpoint. On the bottom are five tetrahedra sharing at least one edge that same centerpoint. There are fifteen objects in all.

I discovered through the work of Lagarias & Zong, the 2015 AMS Conant Award winners, that Aristotle missed the first gap, and it seems everybody missed the octahedral gap.

1. Could these gaps be fundamental to quantum geometries and fluctuations?
2. If so, could there also be domains of perfectly fitting geometries?

Thank you.

Most sincerely,

Bruce

PS Have you seen the interior parts of the octahedron? Just fascinating. The tetrahedron is impressive as well. …the spheres that generate them? I wish I could do it all over again! -BEC